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Journal of Physics A Mathematical and General

One-point functions of the XXZ model and Ramanujan's 1Psi1sum

Katsuhisa Mimachi

Published Jun 21, 1994• 0 citations
Publisher

Abstract

We apply Ramanujan's sum in q-analysis to evaluate the one-point functions of the XXZ model.
DOI
10.1088/0305-4470/27/12/021

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One-point functions for the XXZ model and Ramanujan's 1Ψ1_1\Psi_11​Ψ1​ sum
For any rational number p0≥1p_0\ge 1p0​≥1 we prove an identity of Rogers-Ramanujan-Gordon-Andrews' type. Bijection between the space of states for XXZ model and that of XXX model is constructed.
We show some symmetry relations among the correlation functions of the integrable higher-spin XXX and XXZ spin chains, where we explicitly evaluate the multiple integrals representing the one-point functions in the spin-1 case.We review the multipleintegral representations of correlation functions for the integrable higher-spin XXZ chains derived in a region of the massless regime including the anti-ferromagnetic point.Here we make use of the gauge transformations between the symmetric and asymmetric R-matrices, which correspond to the principal and homogeneous gradings, respectively, and we send the inhomogeneous parameters to the set of complete 2s-strings.We also give a numerical support for the analytical expression of the one-point functions in the spin-1 case.